Consider the problem of powered space flight. The equation giving the kinetic energy obtained by any space vehicle which has been accelerated to a velocity v is of course, K.E. = ½ mv². However observe that to double the velocity of any space vehicle (by increasing v to 2v for example), four times as much energy would be required each time if the laws of the conservation of energy are to be maintained. This results from the relation between velocity and kinetic energy being non-linear. However surely this would go against common sense as the latter would tend to suggest that the formula were as follows, K.E. = mv.

Such an equation would simply state that to increase your velocity by a set amount in the frictionless environment of space the same proportion of energy would be required each time no matter what speed you were travelling at to begin with. The laws of conservation of energy would suggest that the energy supplied to the craft by its power source would at all times equal the kinetic energy obtained, taking into account the various efficiency ratios involved of course. If the kinetic energy did equal ½ mv² then this would result in increasingly larger amounts of fuel being needed to accelerate the craft which in turn would produce a limiting velocity requiring its own separate equation.

Of course we have all been taught since day one that it is actually momentum which equals mv and not kinetic energy. But is it really that straight forward? For example is momentum a force or is it actually a form of energy? Indeed the units it is measured in are rather peculiar, for example kilograms per metre per second. But which do these denote, force or energy?

Consider also that at present the world of physics recognises both the conservation of momentum and the conservation of kinetic energy. However how can both be conserved simultaneously in any given situation if one is equal to mv and the other ½ mv²? One is directly equal to ‘v’ and the other ‘v²’. It doesn’t take a brilliant mathematician to observe that this is clearly impossible.

No, I believe that the current equation for kinetic energy is wrong and should be replaced by the equation for momentum, mv.

But why is the current equation for kinetic energy wrong? This I believe is a result of the equation it is ultimately derived from, Work Done = Force x Distance, which is wrong also. Consider the following two examples:

Two men of exactly the same physical strength push two differing weights mounted on sets of wheels. If the second man pushes his weight for twice the length of time as the first man but with the exact same force surely he would have done twice as much work as a result? However the physics books inform us that this is not actually the case as the accepted relation between work and force is Work Done = Force x Distance.

However the second situation would surely indicate that this accepted relation would never apply. If the weight pushed by the second man is exactly double that of the first’s and is pushed through the exact same distance, each man could not have performed the exact same amount of work while pushing with the same force. On the contrary the second man would have needed to have pushed the heavier weight for a longer duration of time using the exact same force in order to have moved it through the same unit distance (as a result of its acceleration being less from F = ma), and this would have resulted in more work having been done. Again this must be the result of a new relation, Work Done = Force x Time. Our first example would also indicate the same relation.

The equation for kinetic energy is derived from the equation Work Done = Force x Time as follows:

K.E. = W.D. = ∫ F.dx = ∫ m dv/dt . dx = ∫ m dx/dt . dv

= ∫ m v dv = ½ mv²,

However if Work Done is actually equal to Force x Time this would change the existing equation for kinetic energy as follows:

K.E. = W.D. = ∫ F.dt = ∫ m dv/dt . dt = ∫ m dv = mv.

What are the consequences of this?

Well, there are many and I can’t go into them all. However first of all it has to be acknowledged that the current erroneous equation for kinetic energy is used throughout Quantum Physics and Relativity. This fact alone would tend to undermine much of the content of these two schools of thought in the world of physics.

Another stunning consequence is found in the world of astronomy in that meteorites no longer explode on impact. It has always been hotly debated whether the craters on both the Moon and the Earth were volcanic or meteoritic in origin. Certainly some of the low lying craters on Earth are provably volcanic in origin.

While it may have been hotly debated in the past that craters on the moon are volcanic, it hasnt been in quite sometime. Since you can clearly see the ejecta fans around them it is fairly clear that they are impact craters. Not to mention the lack of evidence for any substantial vulcanism at any time in the moons history. In addition, whether or not a meteorite "explodes" on impact or simply dives its way into the ground has far more to do with its composition then with its kinetic energy at impact.

I think you might benefit from a kinematics course at your local community college.

__________________If you are not part of the solution, you are part of the precipitate.

Apparently, he knows how to access the superscript capability and, as proven by his post, he has mastered it.

I might add that all of the members and viewers of the forum are so grateful that Gale has masterd the superscript capability because, without it, he would not be able to provide us with all of those equations and, if he couldn't do that, we would have no clue as to what was talking about.

While it may have been hotly debated in the past that craters on the moon are volcanic, it hasnt been in quite sometime. Since you can clearly see the ejecta fans around them it is fairly clear that they are impact craters. Not to mention the lack of evidence for any substantial vulcanism at any time in the moons history. In addition, whether or not a meteorite "explodes" on impact or simply dives its way into the ground has far more to do with its composition then with its kinetic energy at impact.

I think you might benefit from a kinematics course at your local community college.

There are several different explanations for the ejecta fans on the Moon. My favourite is as follows. The Moon's crust has just solidified and is still thin but as the rest of the Moon solidifies and shrinks as a result, pockets of gas are forced towards the surface causing the solidified surface to bulge into domes. These domes then crack under the pressure causing a sudden release of gas followed by a complete collapse of the dome. The result of this collapse is ejecta fans.

Such unexplained domes, though far smaller in size can be seen on the Moon to this day.

If you believe I have my kinematics wrong then please inform me where my logic is faulty.

Take a look at this image of the Copernicus Crater which famously has extensive 'rays' connected to it which span a large part of the Moon's globe. Does it look as if it were formed by a meteorite?

Take a closer look.

See how the inner parts of its walls consist of a series of collapsed terraces?

See also the central mountain peaks on the crater floor? How were these formed?

See also how flat and level the crater floor is. Why is the floor not curved and bowl shaped at the bottom?

Still convinced it was formed by a meteorite?

In my opinion the terracing is evidence of a domed feature collapsing and this explains the central mountain peaks which 'Bounced back' against the collapse.

You seriously dont know how the peaks in the middle were formed? lol They are prime evidence that this is an impact crater. Its called a central uplift.
As for the collapsed terraces you often to see the ejecta form just such a pattern, especially on Earths moon and other terrestrial bodies in the solar system.
At least try to learn some of the science before spouting off such nonsense.

__________________If you are not part of the solution, you are part of the precipitate.